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Properties

Label 3234.2.x
Level $3234$
Weight $2$
Character orbit 3234.x
Rep. character $\chi_{3234}(491,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 2816 656 2160
Cusp forms 2560 656 1904
Eisenstein series 256 0 256

Trace form

\( 656 q + 4 q^{3} - 164 q^{4} - 5 q^{6} + 8 q^{9} + O(q^{10}) \) \( 656 q + 4 q^{3} - 164 q^{4} - 5 q^{6} + 8 q^{9} - 6 q^{12} + 12 q^{15} - 164 q^{16} - 5 q^{18} - 30 q^{19} + 5 q^{24} + 180 q^{25} - 26 q^{27} + 30 q^{30} + 38 q^{31} - 47 q^{33} - 12 q^{34} - 7 q^{36} + 36 q^{37} + 50 q^{39} - 10 q^{40} - 8 q^{45} - 20 q^{46} + 4 q^{48} + 25 q^{51} - 20 q^{52} - 4 q^{55} - 45 q^{57} + 30 q^{58} - 8 q^{60} + 60 q^{61} - 164 q^{64} + 20 q^{66} - 68 q^{67} + 42 q^{69} + 20 q^{72} + 30 q^{73} + 23 q^{75} + 80 q^{78} + 20 q^{79} + 20 q^{81} + 14 q^{82} - 60 q^{85} + 90 q^{90} + 42 q^{93} - 80 q^{94} - 14 q^{97} - 146 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)